src/daComposant/daAlgorithms/NonLinearLeastSquares.py

   1 #-*-coding:iso-8859-1-*-
   2 #
   3 # Copyright (C) 2008-2017 EDF R&D
   4 #
   5 # This library is free software; you can redistribute it and/or
   6 # modify it under the terms of the GNU Lesser General Public
   7 # License as published by the Free Software Foundation; either
   8 # version 2.1 of the License.
   9 #
  10 # This library is distributed in the hope that it will be useful,
  11 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  12 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13 # Lesser General Public License for more details.
  14 #
  15 # You should have received a copy of the GNU Lesser General Public
  16 # License along with this library; if not, write to the Free Software
  17 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA
  18 #
  19 # See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
  20 #
  21 # Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  22
  23 import logging
  24 from daCore import BasicObjects
  25 import numpy, scipy.optimize
  26
  27 # ==============================================================================
  28 class ElementaryAlgorithm(BasicObjects.Algorithm):
  29     def __init__(self):
  30         BasicObjects.Algorithm.__init__(self, "NONLINEARLEASTSQUARES")
  31         self.defineRequiredParameter(
  32             name     = "Minimizer",
  33             default  = "LBFGSB",
  34             typecast = str,
  35             message  = "Minimiseur utilisé",
  36             listval  = ["LBFGSB","TNC", "CG", "NCG", "BFGS", "LM"],
  37             )
  38         self.defineRequiredParameter(
  39             name     = "MaximumNumberOfSteps",
  40             default  = 15000,
  41             typecast = int,
  42             message  = "Nombre maximal de pas d'optimisation",
  43             minval   = -1,
  44             )
  45         self.defineRequiredParameter(
  46             name     = "CostDecrementTolerance",
  47             default  = 1.e-7,
  48             typecast = float,
  49             message  = "Diminution relative minimale du cout lors de l'arrêt",
  50             )
  51         self.defineRequiredParameter(
  52             name     = "ProjectedGradientTolerance",
  53             default  = -1,
  54             typecast = float,
  55             message  = "Maximum des composantes du gradient projeté lors de l'arrêt",
  56             minval   = -1,
  57             )
  58         self.defineRequiredParameter(
  59             name     = "GradientNormTolerance",
  60             default  = 1.e-05,
  61             typecast = float,
  62             message  = "Maximum des composantes du gradient lors de l'arrêt",
  63             )
  64         self.defineRequiredParameter(
  65             name     = "StoreInternalVariables",
  66             default  = False,
  67             typecast = bool,
  68             message  = "Stockage des variables internes ou intermédiaires du calcul",
  69             )
  70         self.defineRequiredParameter(
  71             name     = "StoreSupplementaryCalculations",
  72             default  = [],
  73             typecast = tuple,
  74             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  75             listval  = ["BMA", "OMA", "OMB", "CurrentState", "CostFunctionJ", "CostFunctionJb", "CostFunctionJo", "Innovation", "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum"]
  76             )
  77         self.defineRequiredParameter( # Pas de type
  78             name     = "Bounds",
  79             message  = "Liste des valeurs de bornes",
  80             )
  81
  82     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
  83         self._pre_run(Parameters)
  84         #
  85         # Correction pour pallier a un bug de TNC sur le retour du Minimum
  86         if self._parameters.has_key("Minimizer") == "TNC":
  87             self.setParameterValue("StoreInternalVariables",True)
  88         #
  89         # Opérateurs
  90         # ----------
  91         Hm = HO["Direct"].appliedTo
  92         Ha = HO["Adjoint"].appliedInXTo
  93         #
  94         # Utilisation éventuelle d'un vecteur H(Xb) précalculé
  95         # ----------------------------------------------------
  96         if HO["AppliedToX"] is not None and HO["AppliedToX"].has_key("HXb"):
  97             HXb = Hm( Xb, HO["AppliedToX"]["HXb"])
  98         else:
  99             HXb = Hm( Xb )
 100         HXb = numpy.asmatrix(numpy.ravel( HXb )).T
 101         #
 102         # Calcul de l'innovation
 103         # ----------------------
 104         if Y.size != HXb.size:
 105             raise ValueError("The size %i of observations Y and %i of observed calculation H(X) are different, they have to be identical."%(Y.size,HXb.size))
 106         if max(Y.shape) != max(HXb.shape):
 107             raise ValueError("The shapes %s of observations Y and %s of observed calculation H(X) are different, they have to be identical."%(Y.shape,HXb.shape))
 108         d  = Y - HXb
 109         #
 110         # Précalcul des inversions de B et R
 111         # ----------------------------------
 112         RI = R.getI()
 113         if self._parameters["Minimizer"] == "LM":
 114             RdemiI = R.choleskyI()
 115         #
 116         # Définition de la fonction-coût
 117         # ------------------------------
 118         def CostFunction(x):
 119             _X  = numpy.asmatrix(numpy.ravel( x )).T
 120             if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 121                 self.StoredVariables["CurrentState"].store( _X )
 122             _HX = Hm( _X )
 123             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 124             if "SimulatedObservationAtCurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 125                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 126             Jb  = 0.
 127             Jo  = 0.5 * (Y - _HX).T * RI * (Y - _HX)
 128             J   = float( Jb ) + float( Jo )
 129             self.StoredVariables["CostFunctionJb"].store( Jb )
 130             self.StoredVariables["CostFunctionJo"].store( Jo )
 131             self.StoredVariables["CostFunctionJ" ].store( J )
 132             return J
 133         #
 134         def GradientOfCostFunction(x):
 135             _X      = numpy.asmatrix(numpy.ravel( x )).T
 136             _HX     = Hm( _X )
 137             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 138             GradJb  = 0.
 139             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 140             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 141             return GradJ.A1
 142         #
 143         def CostFunctionLM(x):
 144             _X  = numpy.asmatrix(numpy.ravel( x )).T
 145             _HX = Hm( _X )
 146             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 147             Jb  = 0.
 148             Jo  = 0.5 * (Y - _HX).T * RI * (Y - _HX)
 149             J   = float( Jb ) + float( Jo )
 150             if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 151                 self.StoredVariables["CurrentState"].store( _X )
 152             self.StoredVariables["CostFunctionJb"].store( Jb )
 153             self.StoredVariables["CostFunctionJo"].store( Jo )
 154             self.StoredVariables["CostFunctionJ" ].store( J )
 155             #
 156             return numpy.ravel( RdemiI*(Y - _HX) )
 157         #
 158         def GradientOfCostFunctionLM(x):
 159             _X      = numpy.asmatrix(numpy.ravel( x )).T
 160             _HX     = Hm( _X )
 161             _HX     = numpy.asmatrix(numpy.ravel( _HX )).T
 162             GradJb  = 0.
 163             GradJo  = - Ha( (_X, RI * (Y - _HX)) )
 164             GradJ   = numpy.asmatrix( numpy.ravel( GradJb ) + numpy.ravel( GradJo ) ).T
 165             return - RdemiI*HO["Tangent"].asMatrix( _X )
 166         #
 167         # Point de démarrage de l'optimisation : Xini = Xb
 168         # ------------------------------------
 169         if type(Xb) is type(numpy.matrix([])):
 170             Xini = Xb.A1.tolist()
 171         else:
 172             Xini = list(Xb)
 173         #
 174         # Minimisation de la fonctionnelle
 175         # --------------------------------
 176         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 177         #
 178         if self._parameters["Minimizer"] == "LBFGSB":
 179             Minimum, J_optimal, Informations = scipy.optimize.fmin_l_bfgs_b(
 180                 func        = CostFunction,
 181                 x0          = Xini,
 182                 fprime      = GradientOfCostFunction,
 183                 args        = (),
 184                 bounds      = self._parameters["Bounds"],
 185                 maxfun      = self._parameters["MaximumNumberOfSteps"]-1,
 186                 factr       = self._parameters["CostDecrementTolerance"]*1.e14,
 187                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 188                 iprint      = self._parameters["optiprint"],
 189                 )
 190             nfeval = Informations['funcalls']
 191             rc     = Informations['warnflag']
 192         elif self._parameters["Minimizer"] == "TNC":
 193             Minimum, nfeval, rc = scipy.optimize.fmin_tnc(
 194                 func        = CostFunction,
 195                 x0          = Xini,
 196                 fprime      = GradientOfCostFunction,
 197                 args        = (),
 198                 bounds      = self._parameters["Bounds"],
 199                 maxfun      = self._parameters["MaximumNumberOfSteps"],
 200                 pgtol       = self._parameters["ProjectedGradientTolerance"],
 201                 ftol        = self._parameters["CostDecrementTolerance"],
 202                 messages    = self._parameters["optmessages"],
 203                 )
 204         elif self._parameters["Minimizer"] == "CG":
 205             Minimum, fopt, nfeval, grad_calls, rc = scipy.optimize.fmin_cg(
 206                 f           = CostFunction,
 207                 x0          = Xini,
 208                 fprime      = GradientOfCostFunction,
 209                 args        = (),
 210                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 211                 gtol        = self._parameters["GradientNormTolerance"],
 212                 disp        = self._parameters["optdisp"],
 213                 full_output = True,
 214                 )
 215         elif self._parameters["Minimizer"] == "NCG":
 216             Minimum, fopt, nfeval, grad_calls, hcalls, rc = scipy.optimize.fmin_ncg(
 217                 f           = CostFunction,
 218                 x0          = Xini,
 219                 fprime      = GradientOfCostFunction,
 220                 args        = (),
 221                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 222                 avextol     = self._parameters["CostDecrementTolerance"],
 223                 disp        = self._parameters["optdisp"],
 224                 full_output = True,
 225                 )
 226         elif self._parameters["Minimizer"] == "BFGS":
 227             Minimum, fopt, gopt, Hopt, nfeval, grad_calls, rc = scipy.optimize.fmin_bfgs(
 228                 f           = CostFunction,
 229                 x0          = Xini,
 230                 fprime      = GradientOfCostFunction,
 231                 args        = (),
 232                 maxiter     = self._parameters["MaximumNumberOfSteps"],
 233                 gtol        = self._parameters["GradientNormTolerance"],
 234                 disp        = self._parameters["optdisp"],
 235                 full_output = True,
 236                 )
 237         elif self._parameters["Minimizer"] == "LM":
 238             Minimum, cov_x, infodict, mesg, rc = scipy.optimize.leastsq(
 239                 func        = CostFunctionLM,
 240                 x0          = Xini,
 241                 Dfun        = GradientOfCostFunctionLM,
 242                 args        = (),
 243                 ftol        = self._parameters["CostDecrementTolerance"],
 244                 maxfev      = self._parameters["MaximumNumberOfSteps"],
 245                 gtol        = self._parameters["GradientNormTolerance"],
 246                 full_output = True,
 247                 )
 248             nfeval = infodict['nfev']
 249         else:
 250             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 251         #
 252         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 253         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 254         #
 255         # Correction pour pallier a un bug de TNC sur le retour du Minimum
 256         # ----------------------------------------------------------------
 257         if self._parameters["StoreInternalVariables"] or "CurrentState" in self._parameters["StoreSupplementaryCalculations"]:
 258             Minimum = self.StoredVariables["CurrentState"][IndexMin]
 259         #
 260         # Obtention de l'analyse
 261         # ----------------------
 262         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 263         #
 264         self.StoredVariables["Analysis"].store( Xa.A1 )
 265         #
 266         if "OMA"                           in self._parameters["StoreSupplementaryCalculations"] or \
 267            "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 268             HXa = Hm(Xa)
 269         #
 270         #
 271         # Calculs et/ou stockages supplémentaires
 272         # ---------------------------------------
 273         if "Innovation" in self._parameters["StoreSupplementaryCalculations"]:
 274             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 275         if "BMA" in self._parameters["StoreSupplementaryCalculations"]:
 276             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 277         if "OMA" in self._parameters["StoreSupplementaryCalculations"]:
 278             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 279         if "OMB" in self._parameters["StoreSupplementaryCalculations"]:
 280             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 281         if "SimulatedObservationAtOptimum" in self._parameters["StoreSupplementaryCalculations"]:
 282             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 283         #
 284         self._post_run(HO)
 285         return 0
 286
 287 # ==============================================================================
 288 if __name__ == "__main__":
 289     print '\n AUTODIAGNOSTIC \n'